WASHINGTON—Vulnerable Senate Democrats have amassed sizable war chests to fend off their Republican challengers this fall, but several GOP rivals are closing the gap, outraising Democrats in the final stretch of last year, new figures show.

In their effort to win control of the Senate, Republicans are targeting seven seats held by Democrats in states that President Barack Obama lost in 2012. A Wall Street Journal analysis of the latest campaign filings shows that may not be easy. The four "red-state...